ON ALMOST η-RICCI-BOURGUIGNON SOLITONS

We investigate a Riemannian manifold with almost eta-Ricci-Bourguignon soliton structure. We use the Hodge-de Rham decomposition theorem to make a link with the associated vector field of an almost eta-Ricci-Bourguignon soliton. Moreover, we show that a nontrivial, compact almost eta-Ricci-Bourguignon soliton of constant scalar curvature is isometric to the Euclidean sphere. Using some results obtaining from almost eta-Ricci Bourguignon soliton, we give the integral formulas for compact orientable almost eta-Ricci-Bourguignon soliton.